Question

The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. What's the approximate probability that the average price for 16 gas stations is over $4.69? O almost zero 0.0142 0.0943 unknown

Answer 1

Given:

$\mu=4.59$

$\sigma=0.1$

$n=16$

By using central limit theorem:

$\mu_{\bar{x}} =\mu=4.59$

$\sigma_{\bar{x}} =\sigma/\sqrt{n}=0.1/\sqrt{16}=0.025$

$P(\bar{x}>4.69) =P(z>\frac{4.69-4.59}{0.025})=P(z>4.00)=1-1.0000={\color{Red} 0.0000}$

Answer 2

P(Y > 4.69) = P(Y - mean > 4.69 - mean)
                  = P( (Y - mean)/(SD/root(N)) > (4.69 - mean)/(SD/root(N))
                  = P(Z > (4.69 - mean)/(SD/root(N)))
                  = P(Z > (4.69 - 4.59)/0.025)
                  = P(Z > 4)
                  = 1 - P(Z <= 4)
                  = 1E-08

ANS:Almost zero.